Let f(x)= cases 2x+3,& x1

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\begin{cases}2x+3,& x<1,\\5,& x=1,\\x^{2}+1,& x>1.\end{cases}

Which one of the following statements about

\displaystyle\lim_{x\to1}f(x)

is correct? (a) The limit exists and equals

5

. (b) The limit does not exist because the left-hand and right-hand limits are unequal. (c) The limit exists and equals

2

. (d) The limit exists and equals

4